Question

Find the greatest number which divides 125,150,300 exactly when increased by 4

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The greatest number which divides 125, 150, and 300 exactly when increased by 4 is 21.

Given: The numbers 125, 150, and 300.

To Find: The greatest number which divides 125, 150, 300 exactly when increased by 4.

Solution:

• We are required to find the greatest number, so we shall find the HCF of the given numbers.

• The HCF after being reduced by a particular number gives us the greatest number which divides a set of numbers when increased by that particular number.

Coming to the numerical, we have,

The numbers 125, 150, and 300.

We need to find the greatest number so we shall find the HCF first using the prime factorization method.

Writing the prime factors of the numbers, we get;

  125 = 5 × 5 × 5

  150 = 2 × 3 × 5 × 5

  300 = 2 × 2 × 3 × 5 × 5

∴ HCF ( 125, 150, 300 ) = 5 × 5

                                      = 25

Now, it is said that the HCF must exactly divide the numbers when increased by 4, so we shall decrease the HCF by that number so that again after increasing it, the original HCF comes.

So, the decreased number is = 25 - 4

                                                 = 21

Hence, the greatest number which divides 125, 150, and 300 exactly when increased by 4 is 21.

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